Un triángulo escaleno siempre es
obtusángulo.

Answer:

$33.60

Step-by-step explanation:

Original price of shirt: $40

Percent discount: 20%

Amount of discount: 20% of $40 = 0.2 × $40 = $8

Price after discount: $40 - $8 = $32

Percent of tax: 5%

Amount of tax: 5% of $32 = 0.05 × $32 = $1.60

Total paid after discount and tax: $32 + $1.60 = $33.60

Answer: Lydia paid the amount of 33.60 dollar

Step-by-step explanation:

Retail price of shirt = 40 dollar

Discount = 20%

Discount value:

=20% of 40 dollar                   [ 20/100 * 40 ⇒ 1/5 * 40 ⇒ 40/5 = 8 ]

= 8 dollar  [ discount value]

Price of shirt after discount :

= 40 - 8

= 32 dollar

As she paid 5% discount on the discounted price ( 32 dollar )

So,  5% of 32 = 1.6 dollar        [ 5/ 100 * 32 ⇒  1/20 * 32 ⇒ 32/20 = 1.6]

Amount to pay = 32( price after discount)  + 1.6 ( Tax)

= 33.60 dollar

A polynomial function of degree n has at most n real zeros and at most n - 1 turning points.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

A polynomial function

Now,

Because of the Fundamental Theorem of Algebra states that a polynomial function of degree n has exactly n complex roots (or zeros), some of which may be repeated or non-real. The number of real roots is equal to or less than the number of complex roots.

A turning point is a point where the graph of the polynomial function changes direction from increasing to decreasing or vice versa. The number of turning points is equal to or less than one less than the degree of the polynomial function. This is because each turning point corresponds to a change in the sign of the first derivative of the function, and the first derivative is a polynomial function of degree n - 1.

Therefore, by the function the answer will be n - 1.

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True. The DMAIC approach, which stands for Define, Measure, Analyze, Improve, and Control, is an effective problem-solving methodology used in Six Sigma.

Step 1: Define: Establish the problem to be solved and the goals of the project.

Step 2: Measure: Collect data related to the problem.

Step 3: Analyze: Analyze the data to identify the root cause of the problem.

Step 4: Improve: Develop and implement solutions to address the root cause of the problem.

Step 5: Control: Monitor the process to ensure that the problem remains resolved and that the improvements are sustained.

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Step-by-step explanation:

X(x+6) - 6(x+6)

X+6x-6x-36

X-36

The volume of the solid generated is \(\frac{117}{3} π\)

To find the volume of the solid generated by rotating the region in the first quadrant enclosed by the curves y = 0, x = 2, x = 5 about the x-axis, we need to use the disk method.

The radius of each disk is given by the distance from the x-axis to the curve y = f(x), which in this case is just the value of x itself since the curves y = 0 and x = 2 bound the region.

So, we can set up the integral as follows:

\(V = \int\limits {x} \,  [a,b] πr^2 dx\)
V = ∫[2,5] πx^2 dx
\(V = \int\limits {x} \,  [2,4] πx^2 dx\)
\(V= π(\frac{125}{3} ) - π (\frac{8}{3} )\)
\(V=\frac{117}{3} π\)

Therefore, the volume of the solid generated is \(\frac{117}{3} π\) cubic units.

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Given:

The vertices of a triangle are \((1,1),(-1,-1),(-\sqrt{3},\sqrt{3})\).

To prove:

The given vertices are the vertices of an equilateral triangle.

Solution:

Distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Let the vertices of the triangle are \(A(1,1),B(-1,-1),C(-\sqrt{3},\sqrt{3})\). Then, by using the distance formula, we get

\(AB=\sqrt{(-1-1)^2+(-1-1)^2}\)

\(AB=\sqrt{(-2)^2+(-2)^2}\)

\(AB=\sqrt{4+4}\)

\(AB=\sqrt{8}\)

Similarly,

\(BC=\sqrt{(-\sqrt{3}-(-1))^2+(\sqrt{3}-(-1))^2}\)

\(BC=\sqrt{(1-\sqrt{3})^2+(1+\sqrt{3})^2}\)

\(BC=\sqrt{(1)^2+(\sqrt{3})^2-2\sqrt{3}+(1)^2+(\sqrt{3})^2+2\sqrt{3}}\)

\(BC=\sqrt{1+3+1+3}\)

\(BC=\sqrt{8}\)

And,

\(CA=\sqrt{(1-(-\sqrt{3}))^2+(1-\sqrt{3})^2}\)

\(CA=\sqrt{(1+\sqrt{3}))^2+(1-\sqrt{3})^2}\)

\(CA=\sqrt{(1)^2+(\sqrt{3})^2+2\sqrt{3}+(1)^2+(\sqrt{3})^2-2\sqrt{3}}\)

\(CA=\sqrt{1+3+1+3}\)

\(CA=\sqrt{8}\)

Clearly, \(AB=BC=CA\).

Since all sides of the given triangle are equal, therefore the given vertices are the vertices of an equilateral triangle.

Hence proved.

Answer:

Step-by-step explanation:

Answer:

\(\bold{ \sf \theta = \dfrac{\pi }{9} , \ \ \dfrac{2}{9} \pi , \ \dfrac{7 \pi }{9}, \ \ \dfrac{8\pi }{9}, \ \dfrac{13\pi }{9}, \ \dfrac{14\pi }{9}}\)

Explanation:

\(\dashrightarrow \ \ \sf 2sin(3\theta) = \sqrt{3}\)

\(\dashrightarrow \ \ \sf sin(3\theta) = \dfrac{ \sqrt{3}}{2}\)

\(\dashrightarrow \ \ \sf 3\theta = sin^{-1}(\dfrac{ \sqrt{3}}{2})\)

[ your calc should be in radian mode [R] ]

\(\dashrightarrow \ \ \sf 3\theta = \dfrac{\pi }{3} , \ \ \dfrac{2}{3} \pi , \ \ \dfrac{7 \pi }{3}, \ \ \dfrac{8\pi }{3}, \ \dfrac{13\pi }{3}, \ \dfrac{14\pi }{3}\)

\(\dashrightarrow \ \ \sf \theta = \dfrac{\pi }{9} , \ \ \dfrac{2}{9} \pi , \ \ \dfrac{7 \pi }{9}, \ \ \dfrac{8\pi }{9}, \ \dfrac{13\pi }{9}, \ \dfrac{14\pi }{9}\)

\(107.18 \ \text{units}^{3}\)

Reviewing the formula:

To find the volume of a cone, we need to use the formula \(\frac{\pi r^{2}h }{3}\)h" represents the height of the cone and "r" represents the radius of the cone.

\(\text{Volume of cone:}\ \frac{\pi r^{2}h }{3}\)

Reviewing the given information:

In the cone, we can see that the height of the cone is 10 units, and the radius of the cone is 3.2 units. Let's substitute the radius and the height of the cone to find the volume.

\(\rightarrow \text{Volume of cone:}\ \frac{3.14 \times 3.2^{2} \times 10 }{3}\)

Finding the volume of the cone:

Now, simplify the expression.

\(\rightarrow \text{Volume of cone:}\ \frac{3.14 \times 10.24 \times 10 }{3}\)

\(\rightarrow \text{Volume of cone:}\ \frac{3.14 \times 102.4}{3}\)

\(\rightarrow \text{Volume of cone:}\ \frac{3.14 \times 102.4}{3}\)

\(\rightarrow \boxed{\text{Volume of cone:} \ 107.18 \ \text{units}^{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\text{Rounded to 2 decimal place})\)

Answer:

Can you please show the questions? It's way more easier

It should be noted that with the equations 6 old printers would produce a batch of comic books in less time.

Using 2 new printers is 27 minutes faster than using 6 old printers.

6 old printers would produce 6*(1/150) = 2/75 of a batch per minute.

2 new printers would produce 2*(1/72) = 1/36 of a batch per minute.

(5/6) * t = 30

(4/2) * t' = 18

Solving for t and t', we get:

t = 36 minutes

t' = 9 minutes

Therefore, using 6 old printers would take 36 minutes to produce a batch of comic books, while using 2 new printers would take only 9 minutes. Using 2 new printers is 27 minutes faster than using 6 old printers.

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Answer:

The distance from A to B is approximately 67.5 km

The bearing of B from A is approximately 86.89°

Step-by-step explanation:

i) The distances and the bearing of the motion of the ship is given as follows;

The distance the ship sails on a bearing of 048° = 30 km

The distance further the ship sails on a bearing of 110° = 42 km

From the drawing of the sailing of the ship created with Microsoft Visio, we have;

∠C = 48° + 70° = 118°

By cosine rule, we have;

c² = b² + a² - 2·b·a·cos(∠C)

From which we have;

c² = 30² + 48² - 2 × 30 × 48 × cos(118°) ≈ 4,556.07810082

c ≈ √(4,556.07810082) ≈ 67.5

The distance from A to B = c ≈ 67.5 km

ii) By sine rule, we have;

a/sin(A) = b/sin(B) = c/sin(C)

∴ sin(A) = a·sin(C)/c

Substituting the values of the variables gives;

sin(A) ≈ 48·sin(118°)/67.5

∠A ≈ arcsin(48·sin(118°)/67.5) ≈ 38.89°

Therefore, the bearing of B from A ≈ 48 + 38.89 = 86.89°.

The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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The SSA congruence scheme does not hold when the congruent angles are obtuse. It is not a valid method for proving triangle congruence in this case.

The SSA (side-side-angle) congruence scheme states that if two sides and the non-included angle of one triangle are congruent to two sides and the non-included angle of another triangle, then the two triangles are congruent. However, this scheme is not valid when the congruent angles are obtuse.

To prove this, let's assume that angle A in triangle ABC is obtuse and angle X in triangle XYZ is congruent to angle A. We can construct triangle ABD such that side BD is congruent to side BC and angle BAD is congruent to angle XYZ. However, we cannot prove that triangle ABD is congruent to triangle XYZ, as there can be multiple solutions for the third side of triangle ABD. Therefore, the SSA scheme is not applicable for proving congruence in the case of obtuse angles.

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Answer:

B

Step-by-step explanation:

center (1/2,-5/2)

radius=1/2

Answer:

Hi, there

Question 1: B. 6x^3(x-6)

Question 2: A. (8x+3)^2

Question 3: A. (5x+9y)(5x-9y)

Question 4: D.(x-2)(x-3)

Step-by-step explanation:

Hope this helps :)

The standard matrix A for T1: R2 -> R3 is: \(A=\left[\begin{array}{ccc}-1&2\\1&-1\\-2&-3\end{array}\right]\). The standard matrix A' for T2: R3 -> R2 is: A' = \(\left[\begin{array}{ccc}1&-1&0\\0&1&-1\end{array}\right]\).

To find the standard matrix A for the linear transformation T1: R2 -> R3, we need to determine the image of the standard basis vectors i and j in R2 under T1.

T1(i) = (-1, 1, -2)

T1(j) = (2, -1, -3)

These image vectors form the columns of matrix A:

\(A=\left[\begin{array}{ccc}-1&2\\1&-1\\-2&-3\end{array}\right]\)

To find the standard matrix A' for the linear transformation T2: R3 -> R2, we need to determine the image of the standard basis vectors i, j, and k in R3 under T2.

T2(i) = (1, 0)

T2(j) = (-1, 1)

T2(k) = (0, -1)

These image vectors form the columns of matrix A':

\(\left[\begin{array}{ccc}1&-1&0\\0&1&-1\end{array}\right]\)

These matrices allow us to represent the linear transformations T1 and T2 in terms of matrix-vector multiplication. The matrix A transforms a vector in R2 to its image in R3 under T1, and the matrix A' transforms a vector in R3 to its image in R2 under T2.

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The experimental probability of rolling a 5 is 25/56, or 0.446.

Probability is a field of mathematics that deals with the chance of certain events happening. It is used to calculate the likelihood of different outcomes in a given situation. Probability helps to make decisions for a variety of real-world applications, such as predicting the weather, deciding whether to invest in stocks and calculating insurance rates. Probability is based on the idea that all outcomes are equally likely, and can be expressed as a number between 0 and 1, where 0 means something is impossible and 1 means something is certain.

The experimental probability is calculated by taking the total number of times a number was rolled and dividing it by the total number of rolls. In this case, the total number of times a 5 was rolled is 25, and the total number of rolls is 56. Therefore, the experimental probability of rolling a 5 is 25/56, or 0.446.

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To draw the horizontal alignment for the curve on that shape on 12D, follow these steps:

Step 1: First of all, we have to determine the horizontal alignment for the curve. The horizontal alignment consists of a series of tangents, curves, and spirals.

Step 2: After that, we have to select the appropriate curve radius for the design speed, the superelevation, and the allowable sight distance.

Step 3: Next, plot the vertical curves with the curve layout. A design speed of 50 mph and a curve radius of 1200 ft will be used in this example.

Step 4: Next, we have to calculate the curve length using the formula Lc = Rθ. Here, Lc is the curve length, R is the radius, and θ is the curve angle. In this case, the curve angle is 4 degrees, so the curve length will be 83.775 ft.

Step 5: Then, we will plot the curve using a tangent-tangent-radius (TTR) method. The TTR method involves drawing a tangent to the curve's point of intersection, then drawing another tangent to the next point of intersection, and finally drawing the curve's arc with the given radius. This process is repeated until the curve's entire length is completed.

Step 6: Finally, label the horizontal and vertical curves, including the stationing and curve radius.

That's how we draw the horizontal alignment for the curve on that shape on 12D.

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Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.

In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.

The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.

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The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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It would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

Dennis' reasoning is incorrect.

To determine the rate of picking apples per minute, Dennis correctly divided the total number of apples (24) by the time it took (6 minutes), resulting in 4 apples per minute. However, his approach to calculating the number of apples that could be picked in 8 minutes is flawed.

Dennis multiplied the rate of picking apples per minute (4 apples) by the given time (8 minutes), assuming that the rate remains constant. This approach would be valid if the rate of picking apples per minute were constant, but in this scenario, it is not necessarily the case.

The rate of picking apples could vary depending on factors such as fatigue, efficiency, or other variables. Therefore, it is not accurate to assume that the rate of picking apples per minute remains the same over a longer duration of time.

To determine the number of apples that could be picked in 8 minutes, it would be more appropriate to multiply the rate of 4 apples per minute by the given time of 8 minutes. This would result in 32 apples, as Dennis correctly stated, but his reasoning behind this calculation was flawed.

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Answer:

Step-by-step explanation:

Answer:

x=15/8

Step-by-step explanation:

Given: 2/3x-1/5x=x-1

Determine LCD: 10/15x-3/15x=x-1

Combine like terms: 7/15x=x-1

Get x on one side only: -8/15x=-1

Divide the coefficient on both sides: x=15/8

Answer:

117.94 Ropani

Step-by-step explanation:

Area Of Rhombus=½×d1×d2

=½×480×250

=60,000m²

1Ropani=508.72 {As Given}

60,000m²=(60,000÷508.72)Ropani

=117.94 Ropani

Answer:

60000 m^2

117.943 ropani

Step-by-step explanation:

the area of rhombus = 250 × 480 ÷2=60000 m^2

60000 m^2 = 117.943 ropani



Answer:

try 1239128981441231241

Step-by-step explanation:

myra

Chris and Jim must replace a total quantity of 17 tyres.

In this problem we must use an inequality of the form f(x) ≥ a, where f(x) is the difference between the number of tyres replaced by Jim and the number of tyres replaced by Chris:

(25/20) · x - x ≥ 3

(5/20) · x ≥ 3

x ≥ 12

Then, the minimum number of tyres to be replaced is n = 15 + 12 = 17 tyres.  

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The critical value for an F-test at α = 2.5% significance with one independent variable and 27 observations is approximately 5.7033. It represents the threshold beyond which we reject the null hypothesis in favor of the alternative hypothesis.

To determine the critical value for an F-test at α = 2.5% significance, we need to know the degrees of freedom associated with the numerator and denominator of the F-statistic.

For an F-test, the numerator degrees of freedom (df1) correspond to the number of groups or treatment conditions minus 1. In this case, since there is only one independent variable, the number of groups is 2 (assuming a standard F-test), so df1 = 2 - 1 = 1.

The denominator degrees of freedom (df2) correspond to the total number of observations minus the number of groups. In this case, we have n = 27 observations and 2 groups, so df2 = 27 - 2 = 25.

Now we can use these degrees of freedom values and the significance level (α) to find the critical value using an F-table or calculator.

Using statistical software or an online calculator, the critical value for an F-test with df1 = 1 and df2 = 25 at α = 2.5% significance is approximately 5.7033 (rounded to four decimal places).

Therefore, the critical value for the F-test at α = 2.5% significance is 5.7033.

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Answer:

6 cifras.

Step-by-step explanation:

Siempre que tengamos un numero que termina en "mil", entonces la primer parte la escribimos y luego ira una coma:

por ejemplo, en "ciento once mil trecientos catorce"

lo separamos en:

"ciento once mil" y "trecientos catorce"

y lo escribimos como:

"ciento once" , "trecientos catorce"

111,314

Ahora que definimos esto, vamos a nuestro problema.

Tenemos el numero "quinientos cincuenta y cinco mil"

El cual podemos escribir como:

555,000

Ahora simplemente podemos contar las cifras, tenemos 6.

las cuales son:

Cientos de miles = CM = 5

Decenas de miles = DM = 5

Un miles = UM = 5

Cientos = C = 0

Decenas = D = 0

Unidades = U = 0